Hello, my name is***** am a qualified lawyer and I will be assisting you with your question today. According to the wording of the contact the employer is able to terminate your contract at any point, whether you are on probation or not. What is required of them is a specific notice period, which in this case is equal to 3 months and which you can either work through or be paid in lieu of notice instead. They have decided to give you payment in lieu of notice here.
Also, as you have been continuously employed at your place of work for less than 2 years then your employment rights will unfortunately be somewhat limited. Most importantly, you will not be protected against unfair dismissal. This means that your employer can dismiss you for more or less any reason, and without following a fair procedure, as long as their decision is not based on discriminatory grounds (i.e. because of gender, race, religion, age, a disability, sexual orientation, etc.) or because you were trying to assert any of your statutory rights (e.g. requesting maternity/paternity leave, etc.). So they are not required to provide any reason for the dismissal or follow a fair procedure, all they have to do is simply give you the notice required under your contract, which they have done.
Therefore, in the absence of any discriminatory reasons they are legally able to terminate your employment in the circumstances.
I'm sorry if this is not necessarily the answer you were hoping for, however I do have a duty to be honest and explain the law as it actually stands. This does mean delivering bad news from time to time. I hope you understand and would be happy to provide any further clarification if needed. If you are still satisfied with the level of service you have received I would be grateful if you could please take a second to leave a positive rating by selecting 3, 4 or 5 starts at the top of the page. Thank you